An analytical solution to an axisymmetric thermoelasticity problem for a long solid cylinder is constructed under the assumption that the thermal properties of the cylinder are presented by arbitrary functions of the radial coordinate.By making use of the direct integration method,the steady state temperature has been determined from the corresponding heat-conduction problem under the thermal loading which can vary within the axial coordinate.The expressions for the stress-tensor components due to the foregoing temperature are obtained and analyzed for different types of inhomogeneity and various thermal loadings.Owing to the explicit analytical form,which appeared to be convenient for both computations and analytical treatment,the obtained solution can be regarded as a benchmark one for the formulated problem.